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Izvestiya: Mathematics, 2021, Volume 85, Issue 2, Pages 262–278
DOI: https://doi.org/10.1070/IM9000 (Mi im9000) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Positive solutions of superlinear elliptic problems with discontinuous non-linearities

V. N. Pavlenkoa, D. K. Potapovb

a Chelyabinsk State University
b Saint Petersburg State University
English version PDF (540 kB) Citations (2)
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DOI: https://doi.org/10.1070/IM9000
Abstract: We consider an elliptic boundary-value problem with a homogeneous Dirichlet boundary condition, a parameter and a discontinuous non-linearity. The positive parameter appears as a multiplicative term in the non-linearity, and the problem has a zero solution for any value of the parameter. The non-linearity has superlinear growth at infinity. We prove the existence of positive solutions by a topological method.
Keywords: superlinear elliptic problem, parameter, discontinuous non-linearity, positive solution, topological method.
Received: 14.12.2019
Revised: 14.07.2020
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2021, Volume 85, Issue 2, Pages 95–112
DOI: https://doi.org/10.4213/im9000
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35J61, 35J25, 35B09, 35A01
Language: English
Original paper language: Russian
Citation: V. N. Pavlenko, D. K. Potapov, “Positive solutions of superlinear elliptic problems with discontinuous non-linearities”, Izv. RAN. Ser. Mat., 85:2 (2021), 95–112; Izv. Math., 85:2 (2021), 262–278
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    English version PDF:22
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    References:42
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